Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
630 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C22⋊C4 | C23×C79 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C79 ◁ C2×C22⋊C4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#2812 | C2 | semidirect |
| 2. C79×#2021 | C2 | semidirect |
| 3. C79×#1607 | C2 | semidirect |
| 4. C79×#1595 | C2 | semidirect |
| 5. C79×#1344 | C2 | semidirect |
| 6. C79×#1343 | C2 | semidirect |
| 7. C79×#1316 | C2 | semidirect |
| 33. C22×D4×C79 | D4 | semidirect |
| 44. C2×C4⋊C4×C79 | D4 | semidirect |
| 65. #95×C79 | D4 | semidirect |
| 66. #95×C79 | D4 | semidirect |
| 75. C24×C79 | D8 | semidirect |
| 246. #12093 | C79 | direct (N × H) |
| 257. #2812 | C2×C79 | semidirect |
| 258. #2021 | C2×C79 | semidirect |
| 259. #1607 | C2×C79 | semidirect |
| 260. #1595 | C2×C79 | semidirect |
| 261. #1344 | C2×C79 | semidirect |
| 262. #1343 | C2×C79 | semidirect |
| 263. #1316 | C2×C79 | semidirect |
| 264. C79 | #12093 | direct (N × H) |
| 290. C22×D4 | D4×C79 | semidirect |
| 301. C2×C4⋊C4 | D4×C79 | semidirect |
| 322. #95 | D4×C79 | semidirect |
| 323. #95 | D4×C79 | semidirect |
| 332. C24 | D8×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#2812 | 2 |
| C79×#2021 | 2 |
| C79×#1607 | 2 |
| C79×#1595 | 2 |
| C79×#1344 | 2 |
| C79×#1343 | 2 |
| C79×#1316 | 2 |
| #12093 | 79 |